Supporting the development of curricular knowledge among novice physics instructorsAmy D. Robertson

Citation: American Journal of Physics 86, 305 (2018); doi: 10.1119/1.5016039View online: https://doi.org/10.1119/1.5016039View Table of Contents: http://aapt.scitation.org/toc/ajp/86/4Published by the American Association of Physics Teachers

PHYSICS EDUCATION RESEARCH SECTION

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Supporting the development of curricular knowledge among novicephysics instructors

Amy D. RobertsonDepartment of Physics, Seattle Pacific University, 3307 Third Avenue West, Seattle, Washington 98119-1997

(Received 10 May 2017; accepted 9 November 2017)

In this paper, my aim is to problematize the invisibility (to instructors) of the purposes of particular

exercises within research-based instructional materials (RBIMs) and to provide one possible

solution to this problem that other teacher educators may adapt for their institutional contexts. In

particular, I show that many RBIMs anticipate and respond to particular (often incorrect) learner

ideas, that teachers often do not recognize this, and that not recognizing this can cause teachers to

miss opportunities to build on learner ideas and/or engage students in scientific practices. I share an

instructional activity I designed that is meant to support teachers—including university physics

Learning Assistants—in recognizing the purposes of particular questions or sequences of questions

within RBIMs, and I illustrate that this activity can be a productive starting place for conversation

about RBIMs. VC 2018 American Association of Physics Teachers.

https://doi.org/10.1119/1.5016039

I. INTRODUCTION

The instructional activity I describe in this paper grew outof an observation I made in my course for undergraduatePhysics Learning Assistants (LAs), who are intellectuallyand relationally competent students that support reform-oriented instruction in introductory physics courses.1

Learning Assistants at my university, Seattle PacificUniversity, support introductory physics courses that useTutorials in Introductory Physics,2 research-based instruc-tional materials (RBIMs) that are designed to develop stu-dents’ conceptual understanding and address specificmisunderstandings.3–5 The development of these instruc-tional materials is extensively documented (e.g., Refs. 3, 4,6–22), such that a well-informed physics educationresearcher can see that particular exercises are designed toaddress specific, documented misunderstandings, or to pro-gressively lead students to particular conclusions about howmotion, tension, waves, etc., work. However, when my LAs(originally) look at these materials, these design choices andstrategies are often invisible to them. For example, severalyears ago, in our weekly content preparation meeting, Iasked LAs to identify the purpose of specific sequences ofquestions within a Tutorial about electric fields. Nearly all ofthe LAs answered that the questions were meant to help stu-dents understand electric fields; none of them identified thata question or sequence of questions were meant to elicit andaddress a particular misunderstanding, or to iteratively builda specific idea within students’ understanding of electricfields. For example, in looking at an exercise that asks stu-dents to rank the electric field at points P and Q (Fig. 1), LAstold me that this exercise was designed to “enhance studentunderstanding of electric fields,” even when I knew the

question was designed to address specific student misunder-standings (e.g., that the electric field at a point is indicatedby the density of the electric field lines, not the proximity ofthe point to a field line). As someone who is deeply commit-ted to teacher agency and choice, it concerned me that LAsdid not seem to understand the motivation for particularTutorials exercises but were still willing to implement themwith fidelity. I wanted to empower them to partner with theTutorials and to make local decisions about the appropriate-ness of particular Tutorials exercises for specific students inspecific moments in time.

In a separate paper,23 I present a case study that docu-ments how I—then the instructor of our preparatory and ped-agogy courses for LAs—supported one cohort of thesestudents in developing knowledge of the purpose of particu-lar questions or sequences of questions within RBIMs, pro-posing this knowledge as a new component of Shulman’scurricular knowledge,85 defined by him as “a particular graspof the materials and programs that serve as ‘tools of thetrade’ for teachers.”24 The process of developing this knowl-edge for this cohort of LAs was rigorous and extensive, span-ning the course of an entire academic year. In this paper, Ipresent an instructional activity that I later designed on thebasis of the insights I gleaned from that year-long process.The instructional activity is meant to make visible that exer-cises within RBIMs are designed for particular purposes, andthat these purposes can be inferred from the structure andcontent of the exercises. I used the activity in my courses forLAs in the following three years that I taught the course, andI found that it streamlined the process of curricular knowl-edge development, such that in two or three class sessionsLAs generated insights that it took my first cohort a fullquarter to develop.86

305 Am. J. Phys. 86 (4), April 2018 http://aapt.org/ajp VC 2018 American Association of Physics Teachers 305

There are many different perspectives about what teachersneed to know or be able to do to teach well.24–29 Here I takethe perspective that teachers (including university physicsTeaching and Learning Assistants) need to develop curricu-lar knowledge—in particular, knowledge of the purposes ofparticular questions or sequences of questions within the cur-ricula they use—and I provide one possible way of begin-ning that process. In what follows, I situate this perspectivein the literature. I then share the instructional activity that Ideveloped and give examples of how novice instructors haveinteracted with it. My aim in writing this paper is to both(a) problematize the invisibility of the purposes that RBIMsare designed to serve and (b) provide a possible solution tothis problem that others may adapt for their own institutionalcontexts.

A. Some research-based instructional materialsanticipate and respond to student ideas

As in the example illustrated by Fig. 1, many RBIMs inphysics anticipate and respond to student ideas.87 As a sec-ond example, the Physics and Everyday Thinking curricu-lum30 includes an activity in which students are asked to (1)draw a model representing the inside of a magnetized nail,(2) predict what will happen to the magnetic properties ofthe (magnetized) nail when it is cut in half, and then (3) per-form the cut-the-nail-in-half experiment. This experiment isintended to address a particular, incorrect model for magneti-zation: as in Fig. 2, learners often predict that like “magneticcharges” congregate on opposite ends of the nail.31 If theoriginal magnetized nail had “N” charges congregated in onehalf and “S” charges congregated in the other, cutting thenail in half would result in an all-“N” and an all-“S” half.Each of these halves would not behave like a magnet—i.e.,would not have differently interacting ends. However, whenlearners perform the cut-the-nail-in-half experiment, theyfind that each half of the nail does behave like a magnet,challenging the incorrect model. In the curriculum, learnersare asked to reconcile their predictions and observations, andthen to revise their original model for the magnetized nail ifthe two conflict.

Similarly, the “Conservation of Momentum in OneDimension” Tutorial2 includes a sequence of questionsintended to address the canonically incorrect understandingof momentum as a scalar.8 The Tutorial poses a hypotheticalsituation in which a less massive glider, A1, moving to theright, collides with a more massive glider, B1, that is initiallyat rest. Figure 3 (reproduced from the Tutorials) depictswhat happens to the motion of the two gliders after the colli-sion. Given this information, students are asked to predictwhether the magnitude of the final momentum of glider B1 isgreater than, less than, or equal to the magnitude of the finalmomentum of the system of both gliders. If a learner consis-tently thinks of momentum as a scalar, they would determinethe magnitude of the momentum of the system by adding themagnitudes of the momenta of gliders A1 and B1, and wouldthus predict that the magnitude of the final momentum of thesystem is less than that of glider B1. The Tutorial seeks toelicit this misunderstanding with the particular scenario itoffers. It addresses this misunderstanding by (1) asking stu-dents to draw “qualitatively correct” vectors for the initialand final momenta of glider A1, glider B1, and the system,providing them the grid in Fig. 4, and then (2) suggestingthat their vector diagrams should be (a) consistent with theprinciple of conservation of momentum and (b) consistentwith their earlier prediction of the relative magnitudes of themomenta of glider B1 and the system.

In both of these examples, RBIMs anticipate that learnerswill use particular misunderstandings in thinking about mag-netism or momentum, and the materials are designed to elicitand then address these misunderstandings. These purposesare communicated to us (the readers) by the structure andcontent of the materials themselves: we can make sense ofthe sequence of activities and the specific directions given tostudents in light of the purpose of addressing particular mis-understandings. However, without an overt awareness thatRBIMs are designed to anticipate and respond to studentideas, these purposes are often invisible to curriculum users;I turn to this next.

B. Curriculum users may not recognize that RBIMsanticipate and respond to student ideas

Many studies have explored curriculum use—which maydraw on curricular knowledge—in science and mathematicsclassrooms, primarily focusing on: articulating the inevitabil-ity of curricular adaptation;32–42 modeling the types of adapta-tions teachers make;35,36,41,43–51 and determining what factorsinfluence teacher adaptations.41,43–46,48–50,52–54 However, tomy knowledge, there is very little in the literature that speaksto the development of teachers’ knowledge of the purposes ofparticular questions or sequences of questions within RBIMs.Harlow’s55,56 characterization of two teachers’ use of the“Models of Magnetism” Physics and Everyday Thinking

Fig. 1. Reproduction of electric field from "Electric Field and Flux," Sec.

III. Reproduced with permission from McDermott et al., Tutorials inIntroductory Physics, Preliminary 2nd ed., 2011, Pearson, p. 95.

Fig. 2. Common adult learner model for unmagnetized (left) and magnetized (right) nails. Reproduced with permission from D. B. Harlow, “Uncovering the

hidden decisions that shape curricula,” in Proceedings of the 2010 Physics Education Research Conference, edited by C. Singh, M. Sabella and S. Rebello.

Copyright 2010, AIP Publishing LLC.

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module (described in Sec. I A) is one notable exception. Inher papers, Harlow compares the implementation of thismodule in Ms. Shay’s and Ms. Carter’s elementary schoolclassrooms. Whereas the curriculum anticipates that learn-ers will model a magnetized nail as having like “magneticcharges” congregated at the two ends of the nail (Fig. 2),students in these two teachers’ classes modeled the magne-tization process as transferring magnetic dust to the nail(Ms. Carter) and as activating something within the nail(Ms. Shay). Ms. Carter recognized the mismatch between(1) the experiment proposed by the curriculum and (2) themodel that her students were using, and she deviated fromthe curriculum, encouraging her students to test their ideaby rubbing their magnetized nails with their fingers to wipeoff the dust. Ms. Shay, on the other hand, followed the cur-riculum as written and instructed her students to cut the nailin half. However, the cut-the-nail-in-half experiment doesnot respond to or challenge the “activation” model for amagnetized nail; in fact, it confirmed this canonically incor-rect model for Ms. Shay’s students. The contrast betweenthese two teachers, Harlow says, highlights the “hidden”-ness of the “decisions that shape curricula.” She writes:

“Looking carefully at the actions of the instructorand curriculum, it is not surprising that Ms. Shayand other teachers may not recognize that cuttingthe nail is in response to the model proposed bythe learners in PET. In fact, the responsive actionof the curriculum is hidden from learners. Thelearners do not know that the curriculumdevelopers anticipated that they would proposethis particular model.”55

On the basis of her analysis, Harlow advocates for moretransparency on the part of curriculum developers withrespect to the decisions that influence the structure and con-tent of research-based instructional materials, and for moreintentional focus on this dimension of teacher understandingin teacher education programs:

“In particular, [teachers] need to learn torecognize when the planned activities are notappropriate and to make real-time instructionaldecisions…Making the knowledge that goes intodesigning activities transparent to teachers mayhelp teachers recognize the underlying structure ofthe activity.”56

Harlow’s work sheds light on what can happen when teach-ers—like Ms. Shay—do not recognize the purposes of particu-lar exercises within RBIMs. She proposes that recognizingthese purposes supported Ms. Carter in successfully modifyingthe curriculum to meet the needs of her own students, facilitat-ing these students’ enactment of sophisticated model-buildingpractices. My own work in supporting LAs in developing cur-ricular knowledge in the context of the Tutorials [documentedin Robertson et al. (submitted)23] suggests that: (a) the purposesof particular exercises within RBIMs are not necessarily obvi-ous to novice instructors (see earlier in Sec. I), and (b) develop-ing curricular knowledge can support novice instructors inenacting flexible instruction,57–60 in ways that are consistentwith recent STEM education reforms61–63 and best-practices inSTEM education pedagogy. By “flexible instruction,” I meaninstruction in which the “actual learning trajectory” differsfrom the “planned learning trajectory,”60 in ways that respondto learner ideas. For example, developing curricular knowledgein the context of the Tutorials supported LAs in:

• prioritizing particular parts of the Tutorial on the basis oftheir assessment of their students’ proximal needs;

• recognizing when students were demonstrating the misun-derstandings the Tutorials were eliciting, and then partner-ing with the Tutorials to address these misunderstandings;and

• deviating from the Tutorials when the conjectures the cur-riculum made were incorrect for specific students.

As an example of the latter, one LA’s decision to tellher students to skip the remainder of a particular

Fig. 3. Collision depicted in the “Conservation of Momentum in One Dimension” Tutorial. Reproduced with permission from McDermott et al., Tutorials inIntroductory Physics, Preliminary 2nd ed., 2011, Pearson, p. 50.

Fig. 4. Grid for drawing momentum vectors for the collision depicted in Fig. 3. Reproduced with permission from McDermott et al., Tutorials in IntroductoryPhysics, Preliminary 2nd ed., 2011, Pearson, p. 50.

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Tutorial section was tied to her sense that studentswere not experiencing the misunderstanding it wasmeant to elicit, confront, and resolve. [For more detail,see Ref. 23.]

These examples illustrate that though it may not beobvious to teachers that RBIMs are anticipating andresponding to student ideas, teachers can develop suchknowledge, either by reflecting on their own experiences,like Ms. Carter did, or by intentional engagement in thedevelopment of curricular knowledge, as my cohort ofLAs did. Further, these examples illustrate that thisknowledge can be consequential to student learning, andthat teacher partnership with RBIMs can be a powerfulmeans by which to accomplish the purposes of RBIMs. Icontinue to flesh out the importance of this kind ofknowledge next.

C. It is important for curriculum users to recognize thatRBIMs anticipate and respond to student ideas

By design, many RBIMs embed pedagogical contentknowledge:24–29 they anticipate and respond to commonlearner ideas, and they use representations and sequencesof questions that “work” for many students. But what ifstudents present unanticipated but fruitful lines of inquiry,or what if the ideas students bring to bear are differentfrom the ones anticipated by the curriculum? Instructors(like Ms. Shay) who do not recognize that the curriculumanticipates and responds to learner ideas may miss out onopportunities to engage their students in scientific practi-ces or to build on learners’ productive (but unanticipated)ideas.

Yet we know that building on learners’ productiveideas59,64,65 and engaging students in practices that center onthe articulation and refinement of ideas about scientific phe-nomena66,67 are important. Opportunities to practice scienceare central to the vision of recent reforms,61 and instructionthat is grounded in students’ thinking is consistent with whatwe know about how people learn.68–70 Further, teaching thattreats students as capable sense-makers have the potential todismantle traditional systems of privilege71,72 by challenginga “dichotomous view” of student thinking (e.g., correct ver-sus incorrect) and instead focusing on the “potentially pro-found continuities between everyday and scientific ways ofknowing and talking.”73 In fact, literature on curriculum useexplicitly acknowledges the importance of balancing respon-siveness to students and use of the curriculum as writ-ten.34–36,42,43,49,51,53,74,75 For example, Brown andEdelson35 treat the balance between curricular adaptationand fidelity as a tension at the center of classroom practice.

Ben-Peretz34 advocates for a view of “curriculumpotential”—i.e., that there are a vast range of possible usesof any given curriculum, and it is the teacher’s role to“uncover” the curriculum’s potential for any given moment,depending on the situation.

Teachers’ recognition of the purposes of particularquestions and sequences of questions within RBIMs alsohas implications for fulfilling those purposes, or partner-ing with the curriculum to accomplish specific instruc-tional goals. Both the literature and my own experiencewith LAs offer examples that support this. For example,Goertzen et al.76 studied university physics TeachingAssistants’ beliefs and practices as they facilitated stu-dents’ completion of worksheets from Maryland Open-Source Tutorials in Physics Sense-Making.77,78 Theyobserved one TA’s—Alan’s—interactions with students inthe context of tutorials that were designed to support stu-dents in reconciling formal physics concepts/principleswith their “common-sense” ideas. The authors note thatAlan regularly constrained the conversation, “fail[ing] toelicit students’ ideas…despite the tutorial’s emphasis oneliciting and refining students’ common sense thinking.”Likewise, in my own observations of LAs’ teachingpractice (and in approximations of their practice), Inoticed that LAs would often correct students in themidst of an extended sequence that was meant to buildunderstanding of a particular concept, pre-empting theconceptual development intended by the curriculum. InRef. 23, we show that LAs’ development of curricularknowledge supported them in choosing when to inter-vene; often, it supported them in waiting to interveneuntil students had an opportunity to experience the cur-riculum as written. For example, one LA, Ellie, wrote inher teaching reflection:

“One group had a question about a difficulty that Iknew was about to be addressed later in thetutorial. So I had them work through it and I cameback to see if they were still having trouble, butthey no longer were. So I used what I knew aboutthe tutorials to decide if I should answer theirquestion now or later.”

Remillard42 presents a vision of curriculum use as partic-ipation with the text, which assumes “that teacher and cur-riculum materials are engaged in a dynamicinterrelationship that involves participation on the parts ofboth teacher and text.” Such a perspective differs from aconceptualization of curriculum use as “following or sub-verting the text,” where teachers are often seen as“conduits” of externally designed curricula. The former of

Fig. 5. Zach’s response to question 6.

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these—participation with the text—is more consistent withthe possibilities I name above, where teachers take upopportunities to build on their students’ thinking, to engagetheir students in the refinement of scientific models, and,when appropriate, to partner with the curriculum to accom-plish its purposes. We saw this in the case of Ms. Carter,whose participation with the curriculum supported her stu-dents in refining their own model of a magnetized nail. Thelatter of these—“following or subverting the text”—maycause teachers to miss such opportunities, or rely exclu-sively on the curriculum to provide such opportunities. Ifeel that such partnership—and all of the potentialtherein—requires teachers to understand the purposes ofthe questions and sequences of questions within the curricu-lum, or to develop the kind of curricular knowledge Ipropose.

II. SUPPORTING LAs IN THINKING ABOUT THE

PURPOSES OF PARTICULAR EXERCISES WITHIN

RBIMs

In my own work as a teacher educator, I have supportedPhysics LAs in developing curricular knowledge in the con-text of the Tutorials in Introductory Physics2 curriculum,discussed above. In this section, I present an instructionalactivity that I use with my LAs that is based on the insights Ihave gleaned over the past five years. In Sec. III, I will shareexamples that illustrate how LAs engage with this activity.Before I do either of these, I briefly offer some context thatmay be important for readers’ understanding (and potentialuse) of this activity.

A. Context

As I briefly say above, Physics Learning Assistants (LAs)at my university—Seattle Pacific University (SPU), a privateliberal arts institution in the Pacific Northwest UnitedStates—are relationally competent students that supportreform-oriented instruction in university physics courses.Like LAs at other institutions, LAs at SPU take a pedagogycourse that focuses on educational theory and best-practicesin facilitating dialogue amongst students. LearningAssistants also take a “prep” course, where they meet to goover the materials that they will teach in the subsequentweek. The instructional activity I describe in this section wasused in our “prep” course. Unlike LAs at many other institu-tions, SPU Physics LAs (during the time I was the courseinstructor) enroll in prep and pedagogy courses each quarterthat they serve as an LA (i.e., not only the first semester orquarter that they serve as an LA). Many—though not all—ofour LAs go on to become K-12 teachers. For those inter-ested, Refs. 23 and 79–83 further describe SPU’s PhysicsLA Program.

B. Instructional activity to develop LAs’ curricularknowledge

The instructional activity I use with LAs is grounded inexamples from the Physics and Everyday Thinking (PET)30

“Models of Magnetism” module (discussed extensivelyabove) and from Harlow’s55 paper that compares Ms.Carter’s and Ms. Shay’s implementation of this module. (Inwhat follows, boxed text indicates pieces of the activityitself.) The activity starts with an overview:

Pre-Assignment: Thinking About How theStructure and Content of CurriculumCommunicates its Purposes

The primary goal of this assignment is to get usthinking about the purposes of particular curricularexercises. Most research-based curricula have thegeneral goal of supporting the development of con-ceptual understanding, but each one goes aboutdoing this in particular ways that communicateadditional purposes and/or values. One of thethings we’ll do this quarter is to think about thepurposes of specific questions (or sets of ques-tions) in the Tutorials being covered each week;I’m hoping this assignment kick-starts thatprocess.

The first set of questions pertains to an activityfrom the curriculum Physics and EverydayThinking, in which students develop a model formagnetism. I won’t ask you to do the entireactivity, but I do want you to get the gist of whatstudents would be asked to do.

The important thing in answering these questionsis that you understand what the students are beingasked and that you’ve thought about your answer.Just write down what you think, intuitively.(We’re not so concerned about the “right” answeras about the content and structure of thecurriculum, and you are definitely not beinggraded on the basis of whether or not your answeris canonically correct.)

In Activity 1 (stated purpose pasted below),students do a series of experiments and observethat an (originally) un-magnetized nail that hasbeen rubbed by a magnet becomes magnetized(i.e., starts to act like a magnet once it has beenrubbed).

The worksheet proceeds with an excerpt from the “Models ofMagnetism” PET module, which states the purpose of Activity 1:

“In Chapter 3 Activity 1, you studied someproperties of the magnetic interaction, inparticular how one magnet can affect anothermagnet. In that activity you discovered that onlycertain materials (ferromagnetic metals) willinteract with a magnet. To remind you of theseproperties, take a moment to review the Scientists’Ideas from that chapter relevant to magnetism.”

But what gives a magnet its properties? Aremagnets made of special material and how arethey made? What is it about ferromagneticmaterials that allows them to interact withmagnets? The purpose of this activity is toinvestigate how you can make a magnet yourself,and to explore in greater depth some additionalproperties of the magnetic interaction. During theremainder of this chapter, you will use thisinformation to construct a model to explainmagnetism.” (p. 4–3, Ref. 30)

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My worksheet then gives LAs the first instruction:

1. In Activity 2, students develop a model for amagnetized nail. Complete the following twopages of this worksheet, which correspond tothe first two pages of Activity 2.

LAs complete pages 4–15 and 4–16 in PET, which instructthem to:

(1) Sketch “what you think might be different about the nail”in the “rubbed” and “unrubbed” conditions, giving themtwo outlines of a nail on which to do so (p. 4–15); and

(2) Explain how their model accounts for their observationsthat: (a) “rubbing an unmagnetized nail with a magnetcan magnetize it”; and (b) “the magnetized nail has northand south poles” (p. 4–15).

LAs are then told to complete two more pages (4–19 and4–20) of the PET “Models of Magnetism” module:

2. The next two pages of Activity 2 ask students todiscuss their drawings and predictions with theirpeers and to decide on a "best model" for therubbed nail (i.e., a consensus model from theirgroup).

Students then predict the behavior of theirrubbed nail (i.e., after it has been magnetized)when it is cut in half. To get a sense for thepredictions that this curriculum is askingstudents to make, complete the following twopages of this worksheet.

Pages 4–19 and 4–20 of PET ask students to reproducetheir sketch of the magnetized nail, assuming that “thepointed end was a north pole” (p. 4–19). Students are thengiven an outline of a nail that has been cut in half and toldto draw “what [their] model above suggests would beinside the two halves” and to “label each end of each pieceaccording to whether it should be a north pole (N), a southpole (S) or have no pole (NoP)” (p. 4–19). They predictwhat would happen if “the north pole of a rubbed nail wasbrought near each of these four ends: attract, repel, ornothing” (p. 4–20) and explain their predictions using theirmodel.

In my instructional activity, after completing pages 4–19and 4–20, LAs see:

3. Students then do the experiment, observe theresults, and modify their models of the rubbednail if necessary.

Follow the prompts on the attached twopages, corresponding to the activity describedabove. In particular, answer the questionasking you to compare your observations andpredictions, and draw your current model ofthe rubbed nail. (Notice that I’ve added theresults you would observe if you conducted theexperiment, assuming — as the worksheetstates — that the rubbed nail was labeled with an“N” at the pointed end and an “S” at the flat end.)

They complete PET pages 4–22 and 4–23, which: (a) pro-vide them with the results of the cut-the-nail-in-half experi-ment (i.e., for each half of the nail, one end is attracted to amagnetized nail and the other end repelled), (b) ask them tocompare their observations with their predictions, and (c) iftheir observations are inconsistent with their predictions,“consider how [they] might change [their] model so it canexplain both [their] new observations and [their] previousobservations” (p. 4–23).

After working through the PET module themselves, LAscomplete the remainder of the worksheet, which is intended to“make visible” that RBIMs anticipate and respond to learnerideas:

4. Thinking about the structure and content ofPET Activities 1 and 2 (which you completedabove), what do you think was the purpose ofthe cut-the-nail-in-half experiment? (i.e.,Why did the authors of this curriculum putthis experiment in this spot?)

5. Please read the two sections (1) “From Learningto Teaching” (including the two sub-sections)and (2) “Discussion” of the paper “Uncoveringthe Hidden Decisions that Shape Curricula,”included in the Blackboard folder with thisassignment. (You can ignore Fig. 3, making thisabout two-pages-worth of reading).

Per your reading, what does Harlow (theauthor) say is the purpose of the experimentin the PET activity you just (partly) did?

What do you think Ms. Carter saw in/understood about the curriculum that Ms.Shay did not?

6. Harlow says that this activity anticipates thatstudents will propose a particular model of therubbed nail and then responds to this modelwith a specific experiment, as though thecurriculum makes decisions or has a mind.

What kinds of decisions do you think theTutorials (used in our intro physics courses)make? Give an example and explain yourthinking.

7. What questions does this assignment raise foryou about the Tutorials curriculum?

In particular, question 4 is intended to both (a) highlight thatspecific activities within an RBIM serve specific purposes and(b) elicit their ideas about what might be the purpose of theexperiment in the PET “Models of Magnetism” module.Question 5 is meant to introduce LAs to Harlow’s comparisonof Ms. Carter’s and Ms. Shay’s implementation of the PETmodule, focusing their attention on her proposal for what theexperiment was designed to do. In answering questions 6 and7, LAs start to think about how these insights might apply tothe RBIMs that they use in their own classrooms.

To be clear, in my courses, this activity is framed as a start-ing place for dialogue about “how RBIMs work;” the conversa-tion does not stop when LAs complete the worksheet. Thespecific form that this dialogue takes depends on the ideas andquestions that LAs bring to bear, in the spirit of participating

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with my own “curriculum.” For example, three years ago, weused the “decisions” LAs proposed (in response to question 6)as a starting place for developing a model for the instructionalstrategies used by the Tutorials; this model became the centerof our discourse for several weeks, and we used it to “dissect”Tutorials and identify which parts corresponded to which strate-gies in our model. Two years ago, we spent two weeks discus-sing LAs’ models for magnetized nails, using this as a platformto talk about what kinds of questions might support learners indeveloping their own models. We then discussed how theexperiment proposed in the PET curriculum responded to thesemodels. And then we sought to answer the question, “Are thereparts of the materials [we’re] using that are anticipating particu-lar ways of thinking from students? What are they? Are thereother specific purposes that the materials are serving?” In everycase, I’ve found the experience of using the activity to be mean-ingful and productive for supporting LAs in both (1) recogniz-ing that RBIMs anticipate and respond to learner ideas and(2) identifying specific instances in which they do so. I willgive examples of what this can look like in Sec. III.

III. ILLUSTRATING LA THINKING ABOUT THE

PURPOSES OF PARTICULAR EXERCISES WITHIN

RBIMs

In this section, I will provide excerpts from LAs’responses to the instructional activity I described in Sec. II,as a way of showing that engaging in this activity can be arich starting place for discussion about the purposes of par-ticular activities within RBIMs. More generally, theseexcerpts—and my own experience of working with noviceinstructors around the development of this kind of knowl-edge23—suggest that novice instructors can develop curricu-lar knowledge of the type I propose. Though I will not claimthat these quotes are representative, neither are they idiosyn-cratic; at least half of my LAs responded in ways that I con-sider to be equally sophisticated.

In particular, it is not uncommon, in the context of thisinstructional activity, for LAs to recognize the purpose of thecut-the-nail-in-half experiment as addressing a particular(canonically incorrect) model for the magnetized nail. Forexample, in response to question 4, LAs wrote:

“The purpose of the experiment was to bring thelearner to a greater understanding of the workingsof a magnet. It would be easy to incorrectly believethat all the (þ) gathered on one side and the (-)gathered at the other. If this model was used thenit would cause the nail, when split, to repel both atone side and attract to both of the other side of thesplit nail. However, when actually done we seethat it is not possible to create an ‘all N’ [or all(þ)] chunk of magnet. It always works in pairs.Also, [the experiment] allowed for the learner togo through the process of creating and checkingsomething, which will allow them to be remindedto check their assumptions as they move forward,especially if their initial diagram was faulty orinsufficient.” (Rusty)88

“I think that the reason the authors put it in therewas to address the misconception of magneticmonopoles contributing to magnetization of anobject. Giving students no instruction, it is fairly

reasonable to assume that there are charge-likeequivalents to magnetic poles, especially if you’vejust done electric polarization. So it is important toaddress this misconception.” (David)

In these responses (and others like them), LAs not only namethe function of the experiment as addressing an incorrectidea, they also identify the specific idea that the experimentis meant to problematize. Further, this idea—that like“magnetic charges” would congregate at either end of thenail (or that “magnetic monopoles would contribute to themagnetization of an object”)—is sensible to them; they rec-ognize this as a reasonable idea for students to bring to bear,given their own experiences.

In reading and responding to Harlow’s analysis, many LAsunderstood the role of curricular knowledge that she proposed.For example, in response to question 5, LAs wrote:

“Ms. Carter knew that by challenging the studentswith the second piece of information, she wouldprompt them to reconsider their ideas and think ofhow they could change their models to make senseof the new observations. Ms. Shay showed themhow to create a model or idea, but not how torevise or develop it when given secondaryinformation.” (Eddie)

“Ms. Carter understood that the purpose of cuttingthe nail in half was to test the model wherecharges separate to the ends. If students proposeanother model, then cutting the nail in half wouldnot help their understanding. So Ms. Carterinstead made up a different experience that wastargeted to the misconceptions in her student’sinitial model.” (Maddie)

Both Eddie and Maddie highlight that Ms. Carter’s instruc-tional choices were responsive to her students’ models inways that the cut-the-nail-in-half experiment was not.

Several LAs articulated ways in which the curriculumthey implement—Tutorials—anticipates and responds tolearner thinking. For example, responding to question 6, LAswrote:

“The Tutorials also follow this model and assumethat there will be a general flow of thought. It willask ‘leading questions’ hoping that the student willanswer a certain way. It will often tell the learnerto make a prediction and then will go through aseries of steps and ask the learner to then reviewtheir prediction and revise it if necessary. Thisseries of steps can be extremely helpful indeveloping the thinking of the learner but it alsocannot, because of its concrete nature due to beingprinted on the page, alter itself to help the learner.This is why it is important to understand what thetutorial is attempting to do in order to helpfacilitate learner participation and maximumbenefit from the classes!” (Rusty)

Rusty’s response draws attention to the fixedness of the cur-riculum and the role this carves out for instructors: since thecurriculum cannot “alter itself to help the learner,” instruc-tors need to understand “what [the curriculum] is attemptingto do” so that they can carry out these purposes in the contextof a dynamic learning environment. Zach’s response,

311 Am. J. Phys., Vol. 86, No. 4, April 2018 Amy D. Robertson 311

illustrated in Figure 5, uses a specific example to illustratehow the Tutorials anticipate and respond to learner ideas: thecurriculum anticipates that learners may think that an objectat rest is not accelerating, and responds to this in the contextof an object on a parabolic trajectory.

Finally, many of the questions that LAs proposed inresponse to question 7 reflected the kind of awareness I washoping to foster, such as what to do when students have ideasthat are different than the ones the curriculum anticipates, orwhat kind of research supports curriculum developers inanticipating student ideas. The first of these is consistentwith the kinds of questions that I raised earlier (in theIntroduction)—e.g., what if the ideas that students bring tobear differ from those anticipated by the curriculum—andcould serve as a “way in” to considering a framing of curric-ulum use as participation with the text (rather than curricu-lum use as following or subverting the text). The secondquestion communicates to me that LAs are becoming awarethat the curriculum is designed with intent, which also repre-sents a step toward considering their own role in relationshipto the curriculum.

In sum, these examples are meant to illustrate: (a) that it ispossible for novice instructors to recognize the purposes ofparticular questions or sequences of questions withinRBIMs, and (b) that the instructional activity I describe canbe a productive starting place for conversations about suchpurposes. Many of the responses in this section speak to theimportance of understanding the purposes of RBIMs, in theways I articulate earlier: LAs acknowledge that students maybring to bear ideas that differ from the ones that the curricu-lum anticipates; they recognize that Ms. Carter’s deviatingfrom the curriculum provided students with opportunities torefine their models; and their vision of their own roles is con-sistent with curriculum use as participation with the text.Teacher educators could use each one of these as a launchingpoint for more conversation—e.g., pressing more deeply intoeach idea, providing opportunities to ground the ideas in par-ticular curricular contexts, etc.

IV. DISCUSSION

In this paper, my aim has been to problematize the invisi-bility (to teachers) of the purposes of particular exerciseswithin RBIMs and to provide one possible solution to thisproblem that other teacher educators may adapt for their owninstitutional contexts. In particular, I have shown that manyRBIMs anticipate and respond to particular (often incorrect)learner ideas, that teachers often do not recognize this, andthat not recognizing this can cause teachers to miss opportu-nities to build on learner ideas and/or engage students in sci-entific practices (whereas recognizing this has had powerfuloutcomes for my own LAs and for Ms. Carter). I shared aninstructional activity I designed that is meant to supportteachers in recognizing the purposes of particular questionsor sequences of questions within RBIMs, and I illustratedthat this activity can be a productive starting place for con-versation about RBIMs.

My own aim in supporting LAs in developing curricularknowledge of this type is to empower them to makeinformed, real-time instructional decisions: I want them toknow what the curriculum is trying to accomplish and todecide if that purpose is what is best for the particular stu-dents in front of them. This is important to me for reasons ofteacher agency—I want teachers to feel capable of and free

to teach in ways consistent with their intuitions and their val-ues. It is also important to me for reasons of student achieve-ment and empowerment—I want students to see their ideasas influential in the direction that their learning takes. Otherteacher educators—with similar goals as mine and/or whoprepare instructors to use RBIMs—may wish to use or adaptmy instructional activity for their local contexts.

Some may object to my focus on the development of cur-ricular knowledge amongst LAs, arguing instead that anotherfocus—such as the development of pedagogical contentknowledge (PCK)24,29,84 or content knowledge—would bemore appropriate. Certainly teacher educators—includingthose who prepare LAs and TAs—must choose among com-peting instructional goals, and I do not wish to dispute theimportance of PCK or content knowledge for teaching.However, I do wish to point out that physics RBIMs them-selves embed both PCK—e.g., in choosing representations tosupport student learning of x idea—and content knowl-edge—e.g., in pressing for deep conceptual understanding ofy idea. Thus, seeking to engage with these materials so as tounderstand what they are designed to accomplish—i.e.,developing curricular knowledge—necessarily providesopportunities for teachers to deepen their content knowledgeand PCK.

Physics education researchers and curriculum developerscan support the development of curricular knowledge by:

• not only providing Instructor’s Guides and other materialsthat make visible the decisions that influence curriculardesign,

• but also by supporting users in developing curriculum-specific curricular knowledge of the kind I advocate forhere. In other words, researchers and curriculum develop-ers could work with users to see that RBIMs anticipateand respond to common learner ideas and/or are meant todevelop particular understandings in specific ways.

These recommendations are consistent with Harlow’s callfor curriculum developers to “mak[e] the knowledge thatgoes into designing activities transparent to teachers” for thepurpose of “help[ing] teachers recognize the underlyingstructure of the activity.”56 However, the second recommen-dation goes beyond Harlow’s suggestion; I am bidding thatcurriculum developers support users in constructing context-specific curricular knowledge, rather than (primarily) dis-seminating that knowledge through instructor’s guides orother facilitation materials.

The instructional activity introduced in this paper drawson my own (and Harlow’s55,56) thinking about two physicsRBIMs—Physics and Everyday Thinking (PET) andTutorials in Introductory Physics. The “Models ofMagnetism” module in PET was sufficiently similar in pur-pose to the Tutorials my LAs were planning to teach that Ifelt it an appropriate starting place for the development ofcurricular knowledge in my context. However, I acknowl-edge the growing diversity of RBIMs in physics; as our fieldcontinues to develop research-based instructional materials,the purposes, structure, and scope of these materials willundoubtedly continue to proliferate. In fact, PET and theTutorials serve very different audiences—future elementaryteachers versus university physics students—and, in manycases, different purposes. This paper is not meant to “cover”the space of RBIM-specific curricular knowledge; instead, Imean to make visible that RBIMs anticipate and respond to

312 Am. J. Phys., Vol. 86, No. 4, April 2018 Amy D. Robertson 312

learner ideas, and to get us thinking about how to supportteachers in developing the knowledge and skills to see this inthe curricula they use. I hope we can broaden this conversa-tion to include more RBIMs, and to consider the implicationsof curricular diversity for the development of curricularknowledge.

ACKNOWLEDGMENTS

This material is based upon the work supported by theNational Science Foundation Grant No. 122732. The authorappreciates the thoughtful feedback offered by StamatisVokos and two anonymous reviewers.

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nition issued by Remillard,42 to mean “printed, often published resources

designed for use by teachers and students during instruction”—e.g., the

Tutorials themselves, in a Tutorials-supported university physics course.86To be clear, this streamlining has advantages with respect to how long it

takes novice instructors to develop this kind of knowledge. However, as I

share in Robertson, Gray, Lovegren, Rininger, and Wenzinger (under

review), taking the time to invent this knowledge had substantive

314 Am. J. Phys., Vol. 86, No. 4, April 2018 Amy D. Robertson 314

advantages for the original cohort (e.g., authentic ownership of their cur-

ricular knowledge).87Many such curricula—and all of the examples I use in this paper—antici-

pate and respond to student misunderstandings. However, some RBIMs in

physics are explicit about their choices to build on students’ productive

resources (e.g., Maryland Open Source Tutorials77,78). Others, including

the Tutorials, though perhaps not explicit, presume students will be able to

iteratively build conceptual models (e.g., for extended light sources) using

existing ideas, thus implicitly treating these existing ideas as productive

resources. I draw on misunderstandings-oriented examples here for rhetor-

ical simplicity—because the instructional activity I developed for LAs and

the literature’s treatment of teachers’ understanding of RBIMs rely on

such examples.88All names are pseudonyms.

315 Am. J. Phys., Vol. 86, No. 4, April 2018 Amy D. Robertson 315